For a class assignment, Andrew wanted to study whether or not the color of a person's car correlates with the color of his or her hair. He spent an hour at a stoplight recording the color of each car that passed and the hair color of its driver.Light hair Dark hairLight car 2 2Dark car 2 4What is the probability that a randomly selected driver has a dark car given that the driver has dark hair?Simplify any fractions.
Question
For a class assignment, Andrew wanted to study whether or not the color of a person's car correlates with the color of his or her hair. He spent an hour at a stoplight recording the color of each car that passed and the hair color of its driver.Light hair Dark hairLight car 2 2Dark car 2 4What is the probability that a randomly selected driver has a dark car given that the driver has dark hair?Simplify any fractions.
Solution
To solve this problem, we need to use the formula for conditional probability, which is P(A|B) = P(A ∩ B) / P(B).
In this case, event A is a driver having a dark car and event B is a driver having dark hair.
P(A ∩ B) is the probability of both events happening, which is the number of dark-haired drivers with dark cars divided by the total number of drivers. From the data, we have 4 dark-haired drivers with dark cars and 10 total drivers, so P(A ∩ B) = 4/10 = 0.4.
P(B) is the probability of a driver having dark hair, which is the total number of dark-haired drivers divided by the total number of drivers. From the data, we have 6 dark-haired drivers and 10 total drivers, so P(B) = 6/10 = 0.6.
Substituting these values into the formula gives us P(A|B) = 0.4 / 0.6 = 2/3.
So, the probability that a randomly selected driver has a dark car given that the driver has dark hair is 2/3.
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